The ideal gas law can also be rearranged to show that the pressure of a gas is proportional to the amount of gas:

Thus the factor RT/V may be used to interconvert amount of substance and pressure in a container of specified volume and temperature.

Equation (1) is also useful in dealing with the situation where two or more gases are confined in the same container (i.e., the same volume). Suppose, for example, that we had 0.010 mol of a gas in a 250-ml container at a temperature of 32°C. The pressure would be

Now suppose we filled the same container with 0.004 mol H2(g) at the same temperature. The pressure would be

If we put 0.006 mol N2 in the container,

Now suppose we put both the 0.004 mol H2 and the 0.006 mol N2 into the same flask together. What would the pressure be? Since the ideal gas law does not depend on which gas we have but only on the amount of any gas, the pressure of the (0.004 + 0.006) mol, or 0.010 mol, would be exactly what we got in our first calculation. But this is just the sum of the pressure that H2 would exert if it occupied the container alone plus the pressure of N2 if it were the only gas present. That is,

Ptotal = pH2 + pN2

We have just worked out an example of Dalton’s law of partial pressures (named for John Dalton, its discoverer). This law states that in a mixture of two or more gases, the total pressure is the sum of the partial pressures of all the components. The partial pressure of a gas is the pressure that gas would exert if it occupied the container by itself. Partial pressure is represented by a lowercase letter p.

Figure 1 The total pressure exerted by a wet gas is equal to the sum of the partial pressure of the gas itself + the vapor pressure of water at that temperature. (At 20°C the vapor pressure of water is 17.3 mmHg.)

Dalton’s law of partial pressures is most commonly encountered when a gas is collected by displacement of water, as shown in Fig. 1. Because the gas has been bubbled through water, it contains some water molecules and is said to be “wet.” The total pressure of this wet gas is the sum of the partial pressure of the gas itself and the partial pressure of the water vapor it contains. The latter partial pressure is called the vapor pressure of water. It depends only on the temperature of the experiment and may be obtained from a handbook or from Table 1.